In manufacturing a semiconductor device, a step of heating a semiconductor substrate rapidly can be necessary. In particular, a high temperature of about 2,000° C. can be needed for annealing to activate a semiconductor substrate having a wideband gap which is typified by a substrate of silicon carbide (SiC). Patent literature 1 describes a back surface electron bombardment heating apparatus. This heating apparatus includes a heating container which includes a heating plate, a reflector, a filament arranged between the heating plate and the reflector, a heating power supply which energizes and heats the filament via two electrodes, and an acceleration power supply which applies an acceleration voltage to the filament. The heating container which includes the heating plate is grounded. The acceleration power supply applies the acceleration voltage between the filament and the heating container so that the filament is at a negative potential. The reflector and the filament are electrically connected to each other, and are at the same negative potential.